Here's two such places I would recommend and have had luck with.
Submittable
Site: submittable.com
Description: Submittable has every writing contest other the sun. Some of its benefits... you can easily keep track of your submissions in the "My Submissions" tab to see what has been reviewed, what's active, and what's been accepted! It helps you stay organized! Also there are different drop down options you can choose to find the contests that you are looking for - like maybe you're looking for "No Fee" "Poetry" "Young Adult" opportunities - you can choose those tags and get to searching!
Caution: Make sure to read the descriptions thoroughly! If a contest sounds "too good to be true" it probably is not a good deal! If a contest makes you pay an arm and a leg just to submit... that's also not usually the type of contest you want to be involved with. There are plenty of legitimate opportunities on Submittable, but you do need to do your research to make sure the opportunity lines up with your expectations for your piece!
Good Stuff: I've had 3 or 4 things published through things I've found on Submittable, and have probably submitted over 30 things there - not every contest you submit to is going to work out, but it's good practice to get your work out there and there are legitimate opportunities if you look for them.
--
Chill Subs
Site: chillsubs.com
Description: Chill Subs is another database of submission opportunities for writers - they have some nice search features like Submittable and also provide a little information about every opportunity that can help you easily browse through things at a quick pace. I LOVE their short descriptions because you can tell at a glance some of the important details.
Caution: Though Chill Subs provides a "little" info, you're still going to want to read the fine-print and full submission guidelines before jumping into a contest. You may even occasionally find opportunities that are no longer active, so be sure to click on the website and get your details before getting your piece ready and spending a bunch of time on a submission.
Good Stuff: Rook and I have had our chicken zine "COOP" posted on Chill Subs for a long time, and a lot of the folks that come across our chicken zine as readers or submitters actually find out about it from Chill Subs. I enjoy that there's some small independent opportunities as well as bigger opportunities available too. There's a ton of variety, so if you're stuck, this is a great place to check out some options! Don't be afraid to consider some of those small off-the-wall zines too
you might get involved with something very cool!---
the fine print
Always read full submission guidelines / requirements / fees before submitting to places! If you're a kid, talk to your mom / dad / guardian before sending personal information or money to a submission opportunity! At the end of the day getting published can take a lot of trial, trial, trial, and error, before success, but there absolutely are legitimate opportunities out there to try out and get your writing into the world!-- Feel Free To Share More Submission Databases / Experiences Below ---